Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x - 5$ and $ BC = 3x + 35$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x - 5} = {3x + 35}$ Solve for $x$ $ 5x = 40$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({8}) - 5$ $ BC = 3({8}) + 35$ $ AB = 64 - 5$ $ BC = 24 + 35$ $ AB = 59$ $ BC = 59$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {59} + {59}$ $ AC = 118$